Sometimes the white spots will disappear when it's left to dry. When you clean shellac you never leave it wet for long, rather use a more suitable polish or sewing machine oil. You can use a cloth well wringed up in water and gently go over the surface, it should be just slighly damp and not leave any wetness on the machine. Shellac in good condition can handle a gentle clean, but be extra careful if you can see wear to decals or flaky shellac.
If the staining is only on the surface you might be able to polish it out with a resin based car polish. I don't know if there are expert tricks for sewing machines, but for wooden furniture I know they use alcohol or lighter fluid, put a match to it and a controlled flame removes white stains. It's rather spectacular first time you see it, and it has to be done very carefully.
On the other hand, there is
this sticky thread on how to repair and improve the finish on old sewing machines. It has given very good results in most cases.